1.1 Subsets of Real Numbers

1.1 Subsets of Real Numbers NO CALCULATOR!!

Real Numbers Real (R) Rational (Q) Irrational (H) Integers (Z) Whole (W) Natural (N) Terminating or repeating decimal {4, –5, 0.02, 0.3333, } {…,–2, –1, 0, 1, 2, …} {0, 1, 2, 3, …} {1, 2, 3, …}

Examples (TWAP)In which sets does each belong? • 2 • 5/8 •  • 1.6 • 0.3333… • –7  N, W, Z, Q, R  Q, R  H, R  Q, R  Q, R  Z, Q, R  H, R

Union & Intersection of Sets • Union of Sets: A  B • in A, in B, or in BOTH • include ALL (don’t repeat) • Intersection of Sets: A  B • must be in BOTH A and B • only include the elements in both sets looks like a “U” looks like an “A” (for AND)

ExamplesA = {0, 2, 3, 4, 6, 9} B = {0, 2, 4, 6, 8, 10} C = {3, 4, 5, 6} all members, but don’t repeat • A  B • C B • (A  B)  C {0, 2, 3, 4, 6, 8, 9, 10} include elements that are only in BOTH {4, 6} {0, 2, 3, 4, 6, 8, 9, 10}  {3, 4, 5, 6} Grouping symbol first! {3, 4, 6}

Examples (TWAP) Let R = {real numbers}, H = {irrational numbers}, Q = {rational numbers}, Z = {integers}, W = {whole numbers}, N = {natural numbers} Find Z  H Find Z  Q 3) Find N  Q 4) Find N  H  (null set) Q Q  (null set)

Homework #101 Pg. 9 1 – 9 odd, 11 – 20 all, 21 – 31 odd

1.1 Subsets of Real Numbers